An important property of the BTN
is that, in the algorithmic implementation and at any iteration step,
only a fixed-sized vector needs to be applied to the representation layer.
We can relate this to brain function: Since the representation layer might occupy a significant portion of the brain, leaving no space for a second concurrent representation, we call this property the “single brain hypothesis” (discussed in more detail in Section ).
Also, due to the nonlinearity of \(\mathbf {g}(\mathbf {a})\) , one breaks the symmetry between subject and object embedding. When we replace the nonlinearity by a linear function, the model cannot distinguish between subject and object.
Simpler models, like TransE [1]} or DistMult [2]} have limited expressibility.
We did not select more standard models for several reasons.
First, most tensor factorizations, such as CPD, the Tucker decomposition, the tensor train, and RESCAL, require the excessive multiplication of factors; multiplication is an operation that is not easily implemented in biological hardware.
Second, standard tensor networks are functions of several embedding vectors which would need to be presented concurrently; this would violate our single brain hypothesis.
Also, our model clearly is compositional (in the sense of [3]}),
which is a property that is used to explain
the superior performance of deep architectures.
